A motorcycle starts from rest and accelerates along a straight line at `2.2(m)/(s^2)`. The speed of sound is `330(m)/(s)`. A siren at the starting point remains stationary. When the driver hears the frequency of the siren at `90%` of when motorcycle is stationary, the distance travelled by the motorcyclist is

Options

A. `123.75 m
B. 247.5 m
C. 495 m
D. 990 m

Answer

B

Explanation

Let `v_m` be the velocity of motorcyclist and v be the velocity of sound.
`v'=(90)/(100)v_0=(v_0(v-v_m))/(v)implies9v=10v-10v_m`
`v_m=(v)/(10)`
`v_m^2-0=2as=(v^2)/(100)`
`S=(v^2)/(200a)=((330)^2)/(200xx2.2)=247.5m`